On the average-case complexity of parameterized clique

Nikolaos Fountoulakis, Tobias Friedrich, Danny Hermelin

Research output: Contribution to journalArticlepeer-review

6 Scopus citations

Abstract

The κ-Clique problem is a fundamental combinatorial problem that plays a prominent role in classical as well as in parameterized complexity theory. It is among the most well-known NP-complete and W[1]-complete problems. Moreover, its average-case complexity analysis has created a long thread of research already since the 1970s. Here, we continue this line of research by studying the dependence of the average-case complexity of the κ-Clique problem on the parameter k. To this end, we define two natural parameterized analogs of efficient average-case algorithms. We then show that k-Clique admits both analogues for Erdős-Rényi random graphs of arbitrary density. We also show that κ-Clique is unlikely to admit either of these analogs for some specific computable input distribution.

Original languageEnglish
Pages (from-to)18-29
Number of pages12
JournalTheoretical Computer Science
Volume576
Issue number1
DOIs
StatePublished - 1 Jan 2015

Keywords

  • Average-case
  • Clique
  • Computational complexity
  • Parameterized complexity

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Computer Science (all)

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